1,276 research outputs found
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and
oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]Comment: Published at http://dx.doi.org/10.1214/009053606000001055 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Generalization error for multi-class margin classification
In this article, we study rates of convergence of the generalization error of
multi-class margin classifiers. In particular, we develop an upper bound theory
quantifying the generalization error of various large margin classifiers. The
theory permits a treatment of general margin losses, convex or nonconvex, in
presence or absence of a dominating class. Three main results are established.
First, for any fixed margin loss, there may be a trade-off between the ideal
and actual generalization performances with respect to the choice of the class
of candidate decision functions, which is governed by the trade-off between the
approximation and estimation errors. In fact, different margin losses lead to
different ideal or actual performances in specific cases. Second, we
demonstrate, in a problem of linear learning, that the convergence rate can be
arbitrarily fast in the sample size depending on the joint distribution of
the input/output pair. This goes beyond the anticipated rate .
Third, we establish rates of convergence of several margin classifiers in
feature selection with the number of candidate variables allowed to greatly
exceed the sample size but no faster than .Comment: Published at http://dx.doi.org/10.1214/07-EJS069 in the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Xiaotong Wang, Violin
Violin Concerto / Robert Schumann; Sonata for Violin and Cello / Maurice Rave
Robust retrieval of material chemical states in X-ray microspectroscopy
X-ray microspectroscopic techniques are essential for studying morphological
and chemical changes in materials, providing high-resolution structural and
spectroscopic information. However, its practical data analysis for reliably
retrieving the chemical states remains a major obstacle to accelerating the
fundamental understanding of materials in many research fields. In this work,
we propose a novel data formulation model for X-ray microspectroscopy and
develop a dedicated unmixing framework to solve this problem, which is robust
to noise and spectral variability. Moreover, this framework is not limited to
the analysis of two-state material chemistry, making it an effective
alternative to conventional and widely-used methods. In addition, an
alternative directional multiplier method with provable convergence is applied
to obtain the solution efficiently. Our framework can accurately identify and
characterize chemical states in complex and heterogeneous samples, even under
challenging conditions such as low signal-to-noise ratios and overlapping
spectral features. Extensive experimental results on simulated and real
datasets demonstrate its effectiveness and reliability.Comment: 12 page
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